Mathematical Contest in Modeling, 2004

The event

The Mathematical Contest in Modeling is an annual event, sponsored by the Consortium for Mathematics and Its Applications, in which students at colleges and universities all over the world are asked to develop and analyze mathematical models of open-ended, practical problems for which no direct solutions are known. Participants work in teams of three and are permitted to use libraries, computers, and other inanimate sources of knowledge and inspiration. The organizers of the contest propose three problems; over the four days of the contest, each team selects one of these problems, designs, implements, and analyzes a model, and writes a substantial report presenting its results.

The twentieth Mathematical Contest in Modeling was held on February 5-9, 2004. Grinnell fielded three teams this year:

The problems

Here are the problems that COMAP posed this year. All three of Grinnell's teams elected to work on problem B.

Problem A: Are fingerprints unique?

It is a commonplace belief that the thumbprint of every human who has ever lived is different. Develop and analyze a model that will allow you to assess the probability that this is true. Compare the odds (that you found in this problem) of misidentification by fingerprint evidence against the odds of misidentification by DNA evidence.

Problem B: A faster QuickPass system

“QuickPass” systems are increasingly appearing to reduce people's time waiting in line, whether it is at tollbooths, amusement parks, or elsewhere. Consider the design of a QuickPass system for an amusement park. The amusement park has experimented by offering QuickPasses for several popular rides as a test. The idea is that for certain popular rides you can go to a kiosk near that ride and insert your daily park entrance ticket, and out will come a slip that states that you can return to that ride at a specific time later. For example, you insert your daily park entrance ticket at 1:15 pm, and the QuickPass states that you can come back between 3:30 and 4:30 pm when you can use your slip to enter a second, and presumably much shorter, line that will get you to the ride faster. To prevent people from obtaining QuickPasses for several rides at once, the QuickPass machines allow you to have only one active QuickPass at a time.

You have been hired as one of several competing consultants to improve the operation of QuickPass. Customers have been complaining about some anomalies in the test system. For example, customers observed that in one instance QuickPasses were being offered for a return time as long as 4 hours later. A short time later on the same ride, the QuickPasses were given for times only an hour or so later. In some instances, the lines for people with Quickpasses are nearly as long and slow as the regular lines.

The problem then is to propose and test schemes for issuing QuickPasses in order to increase people's enjoyment of the amusement park. Part of the problem is to determine what criteria to use in evaluating alternative schemes. Include in your report a non-technical summary for amusement park executives who must choose between alternatives from competing consultants.

Results

This year, 599 teams submitted complete entries. Seven of these entries were judged Outstanding; sixty-one others, Meritorious. One hundred fifty-nine received Honorable Mentions in COMAP's report. The remaining 372 teams were classified as Successful Participants.

Both the team of Doug Babcock, Aditya Bhave, and Jungkan Gu and the team of Arjun Guha, Ogechi Nnadi, and Jihyun Seo earned the rating of Honorable Mention from COMAP's judges. The team of Mike Claveria, Sam Eckstut, and Yvonne Palm was ranked as a Successful Participant.

This document is available on the World Wide Web as

http://www.math.grinnell.edu/mcm-2004.xhtml